Search results

Have questions on searching features :
- is there a way to know what my visitors are searching on my store ?
- is there a way to provide links to specific search results via menu items ?

I tried in analysing the viewed pages url, but search result page url is a generic one (www.mywebsite.com/store/search/result), whatever are the searching keywords of the visitor, so
- is there a trigger I missed to setup the search result url ?
- is there an addon to do this job ?